Units in alternative loop rings
type: Item
instance of: scholarly article
title: Units in alternative loop rings
zbMATH Open document ID: 0594.17016
DOI: 10.1007/BF02772859
author: Edgar G. Goodaire
author: M. M. Parmenter
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Several results concerning units in integral group rings are generalized to the alternative case. Among others, the following interesting theorem is proved: Let \(L\) be a periodic Moufang loop such that the integral loop ring \(ZL\) is alternative. Then every central unit in \(ZL\) is trivial, i.e. belongs to \(L\cup -L\), iff the centre of \(L\) and the factor \(L/L'\) are abelian groups of exponent \(\in \{2,3,4,6\}\).
Mathematics Subject Classification ID: 17D05
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 3955172
zbMATH Keywords: alternative ring
zbMATH Keywords: periodic Moufang loop
zbMATH Keywords: integral loop ring
zbMATH Keywords: central unit
reviewed by: Tomáš Kepka
MaRDI profile type: Publication
cites work: Q5850559
cites work: Loops whose loop rings are alternative
cites work: On the Structure of Group Algebras, I
cites work: Q3322274
cites work: The Units of Group-Rings
cites work: Hamiltonian Loops
cites work: Q5522244
cites work: Q4198893
full work available at URL: https://doi.org/10.1007/bf02772859
OpenAlex ID: W2056238933
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description: scientific article; zbMATH DE number 3955172